A tent is made in the form
of a conic frustum
surmounted by a cone. The
diameter of the base and the
top of the frustum are 14 m
and 7 m and its height is 8 m.
The total height of the tent is
12 m. Find the area of canvas
used to make the tent. (Take
V305 = 17.5 and V113 = 10.6)
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Answer:
Let h be the height of the frustum and r
1
and r
2
be the radii of its circular bases.
We have h=24m,r
1
=10m,r
2
=3m
l= slant height of the frustum
⇒l=
(r
1
−r
2
)
2
+h
2
=
(10−3)
2
+24
2
=25m
for cone VA'B', we have
l
2
= slant height =
O
′
B
′
2
+VO
′
2
=
3
2
+4
2
=5m
Quantity of canvas required
= lateral surface area of frustum + lateral surface area of cone VA
′
B
′
=π(r
1
−r
2
)l+πr
2
l
2
={π(10+3)×25+π×3×5}m
2
=(325π+15π)m
2
=340π m
2
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